DiffEqOperators.jl is a package for finite difference discretization of partial differential equations. It is for building fast lazy operators for high order non-uniform finite differences.
For automated finite difference discretization of symbolically-defined PDEs, see MethodOfLines.jl.
This library is not complete, especially for higher dimensional operators. Use with caution.
For the operators, both centered and upwind operators are provided, for domains of any dimension, arbitrarily spaced grids, and for any order of accuracy. The cases of 1, 2, and 3 dimensions with an evenly spaced grid are optimized with a convolution routine from
NNlib.jl. Care is taken to give efficiency by avoiding unnecessary allocations, using purpose-built stencil compilers, allowing GPUs and parallelism, etc. Any operator can be concretized as an
BandedMatrix or a sparse matrix.